Explanation / Important formulas:
 Cost Price: The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
 Selling Price: The price, at which an article is sold is called its selling prices, abbreviated as S.P.
 Profit or Gain: If S.P. is greater than C.P., the seller is said to have a profit or gain.
 Loss: If S.P. is less than C.P., the seller is said to have incurred a loss
 Gain = (S.P.) – (C.P.)
 Loss = (C.P.) – (S.P.)
 Loss or gain is always reckoned on C.P.
 Gain Percentage: (Gain %) => Gain % = (Gain x 100 / C.P)
 Loss Percentage: (Loss %) => Loss % = (Loss x 100 / C.P)
 Selling Price: (S.P.) => SP = [(100 + Gain %) / 100 x C.P]
 Selling Price: (S.P.) => SP =[(100 – Loss %) / 100 x C.P]
 Cost Price: (C.P.) => C.P = [100 /(100 + Gain %) x S.P]
 Cost Price: (C.P.) => C.P = [100 / (100 – Loss %) x S.P]
 If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.
 If an article is sold at a loss of say, 35% then S.P. = 65% of C.P.
 When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by: % Loss (Common Loss and Gain % / 10)^{2} = (x / 10)^{2}
 If a trader professes to sell his goods at cost price, but uses false weights, then % Gain = [Error / (True Value) – (Error) x 100]%
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Test  Profit and Loss
Profit and loss  Question and Answers
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Question 1

A

10

B

20

C

25

D

30

so, C.P = 4 , S.P = 5
Profit=S.P  C.P, 5  4 = 1
profit % = profit / cost price * 100 then, 1 / 4 * 100 = 25
Question 2

A

16

B

25

C

50

D

None of these

To find profit %, simply minus 12 from 4 = 8
Profit % = 4/8 * 100 = 50
Question 3

A

10

B

11

C

12

D

None of these

To find loss%, simply add 36 to 4 = 40
Loss % = 4/40 * 100 = 10
Question 4

A

10

B

20

C

8

D

12

C.P = 1 * 100/80 = 5/4 on this price we have to gain profit of 20%
So, 5/4 * 120/100 = 3/2
If for Rs. 2/3 we have 12 toffee then for rs 1 we have
= 12 x 2/3
= 8
Question 5

A

110

B

120

C

125

D

150

=> 125/100 * 120/100 * A = 225
=> A = (225 * 2/3)
A = 150
Question 6

A

20%

B

16%

C

25%

D

50%

So, 200gm difference = profit
profit % = 200/800 * 100 = 25%
Question 7

A

10%

B

11%

C

20%

D

21%

(100  110 = 10% on selling)
(110  121 = 10% on buying)
Hence difference = 21 = Profit
Question 8

A

150

B

200

C

250

D

300

then, 10% = rs. 15
100% = rs. 150 , that is your cost price
Question 9

A

25%

B

30%

C

33%

D

33.1/3%

Original price = 25/75 * 100 = 33.1/3%
Question 10

A

5000

B

4800

C

4500

D

5200

Then 20%  16% = 4%
4% = 200 then,
100% = 5000 that is your cost price of the article
Question 11

A

cost = 3.75, profit = 1.87

B

cost = 4.50, profit = 1.50

C

cost = 3.40, profit = 2.50

D

cost = 5.50, profit = 4.50

Selling price = profit = cost
6.00 x 0.25 = 1.50, profit
6.00 – 1.50 = 4.50, cost
Question 12

A

Loss = 34.00, Cost = 20.00

B

Loss = 44.00, Cost = 10.00

C

Loss = 40.00, Cost = 30.00

D

Loss = 30.00, Cost = 20.00

Selling price + loss = cost
50.00 x .60 = 30.00, loss
50.00 – 30.00 = 20.00, cost
Note: To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price
Question 13

A

8.12

B

3.20

C

5.60

D

4.60

7.00 / 1.25 = 5.60, selling price
Note:To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum
Question 14

A

1.00

B

1.50

C

1.60

D

2.40

18 /.12 = 1.50 selling price
Note:To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss
Question 15

A

60%

B

20%

C

30%

D

50%

65 / 1.30 = .5 or 50% profit
Note: To find the percent profit or loss, divide the amount gained or lost by the selling price
Question 16

A

25%

B

27%

C

39%

D

40%

0.20 / 80 = .0025 or 25% loss on selling price
Note: To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.
Question 17

A

.15

B

.12

C

.17

D

.16

.20 / 1.20 = .16666 or .16.67% loss on cost
Note: To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.
Question 18

A

24.5%

B

27.3%

C

37.5%

D

42.3%

.60 / 1.60 = .375 or 37.5% on selling price
Note: To reduce percent markup (percent profit on cost) to percent profit on selling price, divide percent markup by 100% plus percent markup
Question 19

A

65%

B

60%

C

15%

D

75%

From given Expression We take x = 40 , y = 25
Then Gain % = (x  y) x 100 / y
Gain per cent = (40  25)/25 × 100 = 15/25 × 100 = 60%
Question 20

A

36%

B

42%

C

44%

D

48%

CP of 30 bananas = 5 x 5 = Rs. 25
SP of 30 Bananas = 6 x 6 = Rs. 36
Profit = Rs. (36  25) = Rs. 11
Profit % = 11/25 × 100 = 44%
Question 21

A

90

B

100

C

135

D

150

C.P. of 24 oranges = 34/8 × 24 = Rs. 102
S.P. of 24 oranges = 27/12 × 24 = Rs. 114
Gain = 114 – 102 = Rs. 12
Rs. 12 = 24 oranges
Rs. 45 = 24/12 × 45 = 90 oranges
Question 22

A

45 : 56

B

50:61

C

90:97

D

99:125

Printed price = Rs. y
(y * 90)/100=x * 112/100
x/y = 90/112 = 45/56
Question 23

A

2% loss

B

2% gain

C

4% gain

D

4% loss

Loss percent = (20 × 20)/100 = 4%
Question 24

A

215.50

B

212.50

C

240

D

210

Question 25

A

Rs. 40

B

Rs. 45

C

Rs. 50

D

Rs. 35

S.P. at 10% loss = x * 90/100 = Rs. 9x
S.P. at 12 1/2 % gain
x * (100+12.1/2)/100 = Rs. 225x / 200
According to the question, 9x + 9 = 225x / 200
180x + 1800 = 225x
x = Rs. 40
Question 26

A

1000

B

1600

C

2000

D

2500

x * 110/100 * 130/100 = 2860
x = (2860 * 100 * 100) / (110 * 130) = Rs. 2000
Question 27

A

4

B

2

C

3.5

D

2.5

r1 = 20 , r2 = 15
Formula =[(r1 – r2) – (r1 x r2) /100]
[(20  15)  (20 × 15) /100]
= 20  18
= 2%
Question 28

A

Rs. 200

B

Rs. 25

C

Rs. 400

D

Rs. 250

105% of x – 80% of x = Rs. 100
25% of x = Rs. 100
x = Rs. (100 × 100) / 25
x = Rs. 400
Question 29

A

1%

B

2%

C

3%

D

4%

S.P. = 28.60
Gain = 28.60  27.50 = Rs. 1.10
Gain%=(GainCost ∗ 100)% = (1.1027.50 ∗ 100)% = 4%
Question 30

A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the lost percent?
A

10%

B

20%

C

25%

D

28%

S.P. = 4000
Loss = 5000  4000 = 1000
Loss% = (Loss Cost ∗ 100)% = (10005000 ∗ 100)% = 20%
Question 31

A

Rs.1200

B

Rs. 1230

C

Rs. 1260

D

Rs. 1290

(100  loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(951140=105x)
=> x=1260
Question 32

A

2% Profit

B

3% Profit

C

2% Loss

D

3% Loss

So, C.P. = (100110 ∗ 25.75)When S.P. = 25.75 then
Profit=25.75 − 25 = Re.0.75
Profit%=0.7525 ∗ 100=3%
S.P. = (100 + gain%100 ∗ C.P)So,
C.P. = (100110 ∗ 25.75)When S.P. = 25.75 then Profit = 25.75 − 25=Re.0.75
Profit%=0.7525 ∗ 100 = 3%
Question 33

A

150%

B

200%

C

300%

D

350%

Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = 75/25 * 100 = 300
Question 34

A

Rs 15

B

Rs 20

C

Rs 22

D

Rs 25

Let Marked price = Rs X
then 85% of X = 18.70
=> X = 1870 / 85 = 22
Question 35

A

18%

B

20%

C

22%

D

24%

then, Marked price = Rs 135
Required gain = 8%,
So Selling price = Rs 108
Discount = 135  108 = 27
Discount% = (27/135) * 100 = 20%
Question 36

A

Rs 8.81

B

Rs 9.81

C

Rs 11.81

D

Rs 7.2

x = (9 × 105 / 85)
x = Rs 11.81
Question 37

A

Rs. 750

B

Rs. 800

C

Rs. 850

D

Rs. 900

Then, as per question,
=>(125100∗115100∗110100∗P)=1265
=>253160P=1265
=>P=800
Question 38

A

12%

B

13%

C

14%

D

15%

Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150
Selling price = Rs. (8 x 21) = Rs. 168
Profit = 168  150 = 18
So, Profit % = (18/150) * 100 = 12%
Question 39

A

4%

B

5%

C

6%

D

7%

Question 40

A

20%

B

21%

C

22%

D

23%

=[(100 + 10)^{2 }/ 100) − 100]%
= [(12100 – 10000) /100]%
= 21%Gain
Question 41

A

51:52

B

52:53

C

53:54

D

54:55

Required ratio = (104% of x) / (106% of x)
= 104 / 106
= 52 / 53
= 52:53
Question 42

A

130%

B

140%

C

150%

D

160%

Then S.P. = (120 / 100)x = 6x / 5
New S.P. = 2 (6x / 5) = 12x / 5
Profit = 12x / 5  x = 7x / 5
Profit% = (Profit / C.P.) * 100
=> (7x / 5) * (1 / x) * 100
=> 140 %
Question 43

A

12%

B

30%

C

50%

D

60%

Cost of 8 pens = Rs 8
Selling price of 8 pens = 12
Gain = 12  8 = 4
Gain%=(GainCost ∗ 100)% = (48 ∗ 100)% = 50%
Question 44

A

14

B

15

C

16

D

17

S.P. of x articles = Rs. 20
Profit = Rs. (20  x)
Therefore, [(20  x / x) * 100 = 25]
=> 2000  100x = 25x
=> 125x = 2000
=> x = 16
Question 45

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A

70%

B

80%

C

90%

D

None of these

Then, Profit = Rs. 320,
S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420
Profit = Rs. (420  125) = Rs. 295
Required percentage = (295 / 420) * 100
= 70%(approx)
Question 46

If the cost price of 12 items is equal to the selling price of 16 items, the loss percent is?
A

20%

B

25%

C

30%

D

35%

Cost Price of 16 items = 16
Selling Price of 16 items = 12
Loss = 16  12 = Rs 4
Loss % = (4 / 16) * 100 = 25%
Question 47

A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was?
A

Rs 100

B

Rs 150

C

Rs 200

D

Rs 250

Its Selling price = 105 / 100 * x = 21x / 20
New Cost price = 95 / 100 * x = 19x / 20
New Selling price = 110 / 100 * 19x / 20 = 209x / 200
[(21x / 20)  (209x / 200)] = 1
x = 200
Question 48

A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item?
A

Rs. 660

B

Rs. 760

C

Rs. 860

D

Rs. 960

it means S.P. = (100  x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100  x)% of C.P
= 80% of 1200
= 80/100 * 1200
= 960
Question 49

A

Rs. 22000

B

Rs. 24000

C

Rs. 26000

D

Rs. 28000

C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Question 50

A

Rs 25300

B

Rs 22300

C

Rs 24300

D

Rs 21300

85 : 18700 = 115 : x , [as loss = 100 15, Profit = 100 +15]
x = (18700 * 115) / 85
x = Rs. 25300
Question 51

A

45

B

50

C

55

D

60

C.P. of 12 balls = S.P. of 17 balls = Rs.720
C.P. of 1 ball = Rs 720 / 12= Rs. 60
Question 52

A

21,000

B

24,000

C

25,300

D

25,800

x = 18700 x 115 / 85 = 25300
Hence, S.P. = Rs. 25,300
Question 53

A

30

B

40

C

50

D

44

S.P. of 30 articles = Rs. (6 / 5) x 30 = Rs. 36
Gain % = (11 /25) x 100% = 44%.
Question 54

A

3.5

B

4.5

C

5.6

D

6.5

Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33  31.25) = Rs. 1.75
Profit % = (1.75 / 31.25 * 100)%
= 28 / 5% = 5.6%
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